The planned research investigates the initial nature and the development of the concept of number in humans, with emphasis on its mental representation. Initial studies in this laboratory have shown that 5- month-olds can determine the results of simple additions and subtractions of physical objects (e.g., they know that one object added to another identical object results in 2 such objects). Five main issues will be addressed: (1) The first series of studies investigates the extent and developmental progression of infants' knowledge of arithmetical relationships. (2) Nothing is yet known of infants' ability to represent continuous quantity (e.g., amount of substance); the quantificational processes underlying their arithmetical abilities may be specific to discrete quantities (e.g., numbers of individual objects), or they may apply to continuous quantities as well. Series 2 investigates whether infants possess an ability to quantify continuous amounts, and, if so, whether this ability stems from the same underlying processes as does their ability to quantify discrete amounts or if they are two distinct quantificational mechanisms. (3) Series 3 investigates the structure of the mental representations resulting from infants' arithmetical calculations, by seeing how generalizable they are to perceptually different situations. Infants' arithmetical abilities may be inextricably tied to their tracking of individual objects through space; if so, one would expect them to have a situation-specific structure (e.g., "a red cup and another red cup"). If, however, they are truly numerical representations that infants are capable of manipulating numerically, they should not depend on situational properties (e.g., a representation of 'two red cups' that includes a situation-general component is "two red cups'; another is "xx red cups"). (4) Series 4 addresses what constitutes for infants a discrete, countable individual. There is evidence that infants can determine the numerosity, not only of sets of physical objects, but of sequences of sounds as well. Yet little is known about how infants individuate sounds, though much is known about infants' individuation of physical objects. The experiments in series 4 examine infants' individuation of entities such as sounds and actions. (5) Finally. series 5 examines the structure of children's early mental representation of number in a somewhat different manner, by studying preschoolers' acquisition of the linguistic counting system. These issues relate to health concerns in a broad way; by developing a detailed and accurate understanding of the typical course of cognitive development and of underlying cognitive processes, we will be better able to understand and address the problems of populations whose cognitive development and processes deviate from the norm.